On Sun, 13 Jun 1999, Charles J. Cohen wrote:
> But there are infinities that are greater than others. Here is an
> example.
>
> Consider the set of counting numbers: 1, 2, 3, ... etc. That is one
> infinity.
>
> Now consider the set of rational numbers. There are an infinite
> number of rational numbers between each consequtive pair of counting
> numbers (for example, between the nubmers 1 and 2, there are an
> infinite number of ration numbers, such as 3/2, 4/3, 5/4, 6/5, etc.,
> and many many more I could think of. Therefore, the infinite set of
> rational numbers is larger than the infinite set of counting numbers!
Pardon a semi-educated question, but is this a recent
discovery/interpretation? When I learned about the mathematics of
infinities (via PBS/Nova :) in the 80s, one of the specific examples
given was that there were as many counting numbers as rational
numbers, and that the set of rational numbers had as many members
as the set of counting numbers.
The proof presented then was that you could create a
algorithm to equate any member of one set with a unique corresponding
member of the other.
Xavier
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Jim McAdams | Do,
jmcadams@interaccess.com | or Do Not.
630-859-6902 | There is no "Try". - Yoda
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From: James Mcadams <jmcadams@interaccess.com>
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Received on Mon Jun 14 13:55:45 1999
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